I did a similar problem and got it right but I can't seem to get this right:
You are visiting your friend Fabio's house. You find that, as a joke, he filled his swimming pool with Kool-Aid, which dissolved perfectly into the water. However, now that you want to swim, you must remove all of the Kool-Aid contaminated water. The swimming pool is round, with a 10 foot radius. It is 11.5 feet tall and has 3 feet of water in it.
How much work is required to remove all of the water by pumping it over the side? Use the physical definition of work, and the fact that the weight of the Kool-Aid contaminated water is .
So I know that Volume= 100 pi dy
Mass=100pi* dy * 65lb/ft^3
Force = 100pi* dy * (65lb/ft^3) * 9.8 (gravity)
So Work= 100pi* dy * (65lb/ft^3) * 9.8 (gravity) (11.5-y)
work=63700 pi intregal (11.5-y)dy ( from 0 to 3)
work=63700pi (11.5y-(y^2)/2) ( from 0 to 3)
63700pi *30 lb/ft
What did I do wrong?